Diffusion limits for shortest remaining processing time queues

Abstract

We present a heavy traffic analysis for a single server queue with renewal arrivals and generally distributed i.i.d. service times, in which the server employs the Shortest Remaining Processing Time (SRPT) policy. Under typical heavy traffic assumptions, we prove a diffusion limit theorem for a measure-valued state descriptor, from which we conclude a similar theorem for the queue length process. These results allow us to make some observations on the queue length optimality of SRPT. In particular, they provide the sharpest illustration of the well-known tension between queue length optimality and quality of service for this policy.

Cite this work

No public copy is stored for this record, so only the metadata is cited.

Stored only when both papers are in the corpus — 15 citations exist upstream.

Papers that cite the same references — the relational fallback while embeddings are still backfilling.